The figure consists of a quarter circle and a parallelogram. What is the area of the composite figure? Use 3.14 for n 76, Round to the nearest whole number.

A 70 in.2
B 84 in.2
C 154 in.2
D 224 in.2

Answer:

Step-by-step explanation:

y = negative 6 (x minus one-fourth) squared + nineteen-eighths

Step-by-step explanation:

y = –6x^2 + 3x + 2

Divide the first 2 terms of the right side by -6:

y = -6(x^2 - 1/2x) + 2

Now complete the square on the expression in the brackets:

y = -6[(x - 1/4)^2 - 1/16] + 2

y = -6(x - 1/4)^2 + 6/16 + 2

y = -6(x - 1/4)^2 + 38/16

y = -6(x - 1/4)^2 + 19/8

Answer: C

Step-by-step explanation:

Answer:

$18.Hope it helps.....

Random sampling is the selection of clusters first from the community. Then the correct option is C.

Random sampling is the method of selecting the subset from the set to make a statical inference.

A researcher for an airline interviewed all of the passengers on five randomly selected flights.

Cluster sampling is a strategy in which the research splits the overall population into distinct clusters (groups).

Then random sampling is the selection of clusters first from the community.

More about the sample method link is given below.

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Answer:

4x+5y=-12

-2x+3y=-16 ×2

-----------------

eliminate x

4x+5y=-12

-4x+6y=-32

---------------+

11y=-44

y=-44/11

y=-4

y=-4 --->

-2x+3(-4)=-16

-2x-12=-16

-2x=-4

x=-4/-2

x=2

Answer:

7-4g

Step-by-step explanation:

let the number =g

four times the number = 4×g = 4g

seven decreased br four times the number= 7- 4g

therefore, the answer = 7-4g

Answer:

1/5

Step-by-step explanation:

there are 15 pens totally, there are 3 red pens.

probability-> 3/15=1/5

Answer:

Consider the following statements, Each box of 100 pads of an orange-u happy costs$5 to manufacturer. The variable costs for manufacturing q boxes at 100 pads will be V=5.4

Step-by-step explanation:

Answer: I think it’s $15.71

Step-by-step explanation:

Answer:

red I think

Step-by-step explanation:

Answer: i think option c

Step-by-step explanation:

Answer: z=29 x=119 y=61

Step-by-step explanation:

A ray is 180 degrees and you can go from there. Hope this helps!

Answer:

1. right, 2. median, 3. range or the IQR

Step-by-step explanation:

Answer:

For the answers, it would be: 1. right, 2. median, and 3. range or IQR.

a. (40%^5)=0.4^5=0.01024, which is 1.024%

b. the probability that he turns is light off is the probability that he doesn't turn his light on, which is 1-0.4=0.6.

0.6^5=0.07776, or 7.776%

c. 1-0.07776=0.92224, or 92.224%

Answer:

a. 40% = 0.4 → (0.4)⁵ = 0.01024.. ≈ 1.02%.

b. (1 - 0.4) → (0.6)⁵ = 0.07776.. ≈ 7.78%

c. (0.4)¹ → 0.4 = 40%

Explanation:

decimal × 100% = percent.

Since these independent events either occur or do not occur, we can use binomial distribution to determine the theoretical probability of either outcome with a given number of successes or failures (total - successes) or by probability → 1 - success probability = failure probability.

Since the problem is either looking for all or none, we can narrow n! / (n - x)!x! p^x q^n-x down to (probability)^(days). All the rest cancels out.

The experimental probability that the bottle landed on its base by the data recorded is; 3/10.

It follows from the frequency recorded for the bottle landing on it's base and side that; base = 9 and side = 21.

The total possible outcome is 30.

On this note, the required probability is; 9/30 = 3/10.

Read more on probability;

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Answer:

[tex]x = \dfrac 32, ~ x = -4[/tex]

Step by step explanation:

[tex]~~~~~~~2x^2+5x-12=0\\\\\implies 2x^2 +8x-3x-12=0\\\\\implies 2x(x+4) -3(x+4) = 0\\\\\implies (2x-3)(x+4) = 0\\\\\implies 2x -3 = 0~~~~ \text{or}~~~~~~~~ x +4 = 0\\\\\implies 2x = 3~~~~~~~~~ \text{or}~~~~~~~~x = - 4\\\\\implies x = \dfrac 32~~~~~~~~~~ \text{or}~~~~~~~~x = - 4\\\\\text{Hence,}~ x = \dfrac 32, ~ x = -4[/tex]

Taking into account the definition of a system of linear equations:

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

The cost of 3 rackets and 2 squash balls is £26.57.

The cost of 5 rackets and 7 squash balls is £52.90.

So, the system of equations to be solved is

[tex]\left \{ {{2x+3y=26.57} \atop {7x+5y=52.90}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable x from the first equation:

[tex]x=\frac{26.57 - 3y}{2}[/tex]

Substituting the expression in the second you get:

[tex]7\frac{26.57 - 3y}{2}+5y=52.90[/tex]

Solving:

[tex]\frac{7}{2}(26.57 - 3y)+5y=52.90[/tex]

[tex]\frac{7}{2}x26.57 - \frac{7}{2}x3y+5y=52.90[/tex]

92.995 - 10.5y +5y= 52.90

92.995 - 5.5y= 52.90

- 5.5y= 52.90 -92.995

- 5.5y= -40.095

y= (-40.095)÷ (-5.5)

y= 7.29

So: [tex]x=\frac{26.57 - 3y}{2}=\frac{26.57 - 3x7.29}{2}[/tex]

x= 2.35

Finally, the cost of a squash ball and a racket are £2.35 and £7.29 respectively.

In this case, a system of linear equations must be proposed taking into account that:

The cost of 4 kg of radishes and 1.5 kg of carrots is £14.80.

The cost of 3 kg of radishes and 2 kg of carrots is £12.50.

So, the system of equations to be solved is

[tex]\left \{ {{4x+1.5y=14.80} \atop {3x+2y=12.50}} \right.[/tex]

You can solve this system using the substitution method. Isolating the variable x from the first equation:

[tex]x=\frac{14.80 - 1.5y}{4}[/tex]

Substituting the expression in the second you get:

[tex]3\frac{14.80 - 1.5y}{4}+2y=12.50[/tex]

Solving:

[tex]\frac{3}{4}(14.80 - 1.5y)+2y=12.50[/tex]

[tex]\frac{3}{4}x14.80 - \frac{3}{4}x1.5y+2y=12.50[/tex]

11.1 - 1.125y +2y= 12.50

- 1.125y +2y= 12.50 - 11.1

0.875y=  1.4

y= 1.4 ÷0.875

y=1.6

So: [tex]x=\frac{14.80 - 1.5y}{4}=\frac{14.80 - 1.5x1.6}{4}[/tex]

x= 3.1

Finally, the cost of 1 kg of radishes and 1 kg of carrots are £3.1 and £1.6 respectively.

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Answer:

1.) 700 centimeters

2.) 8000 meters

3.) 650 millimeters

4.) 200 centimeters

5.) 7000 meters

6.) 800 centimeters

7.) Just multiply each number by 1000

8.) multiply each by 100

Step-by-step explanation:

Answer:

3.6 in

Step-by-step explanation:

1/2 ft= 6in

1/5 ft= 2.4 in

so 6-2.4= 3.6 in

Hope this helps :)

Answer:

25%

Step-by-step explanation:

Answer:

x= y−2/3

Step-by-step explanation:

1 Subtract 2 from both sides.

y-2=3x

2 Divide both sides by 3.

y−2/3 =x

3 Switch sides.

x= y−2/3

Answer:

c

Step-by-step explanation:

Answer:

How many hours a week do you watch televison?

Step-by-step explanation:

In order for Mike to organize a survey about this particular topic, it's important that he asks concise questions that provide him with generalized data about multiple days of the week. Because of this, he wouldn't want to ask any questions that solely focus on specific days, so we can use process of elimination to get rid of answer choices C and D. Both of these options are too specific, and only ask about 1 or 2 days instead of a larger period of time. Using the same logic, we can get rid of option A. Option A is also too specific, but for a different reason. This question is only asking about students who watch televison for an hour everyday. Remember, for good surveys, more results provide a better sample of data. So it's important that the questions asked are coherent, but also don't limit the amount of data received either.

use tan since you are given the opposite and adjacent sides

tan θ = [tex]\frac{opp}{adj}\\\\[/tex]

tan θ = [tex]\frac{2}{12}[/tex]

use the inverse of tan to find the angle

θ = [tex]tan^{-1}(\frac{2}{12})[/tex]

θ = 9.462322208...

θ = 9.46°

Answer:

[tex]\textsf{13)} \quad y=(x+5)^2+4[/tex]

[tex]\textsf{14)} \quad y=-\dfrac{1}{2}(x-2)^2-3[/tex]

Step-by-step explanation:

Vertex form of a parabola:  

[tex]y=a(x-h)^2+k[/tex]  where (h, k) is the vertex

From inspection of the graph, the vertex is (-5, 4)

[tex]\implies y=a(x+5)^2+4[/tex]

To find [tex]a[/tex], substitute the coordinates of a point on the curve into the equation.

Using point (-4, 5):

[tex]\implies a(-4+5)^2+4=5[/tex]

[tex]\implies a(1)^2+4=5[/tex]

[tex]\implies a+4=5[/tex]

[tex]\implies a=1[/tex]

Therefore, the equation of the parabola in vertex form is:

[tex]y=(x+5)^2+4[/tex]

From inspection of the graph, the vertex is (2, -3)

[tex]\implies y=a(x-2)^2-3[/tex]

To find [tex]a[/tex], substitute the coordinates of a point on the curve into the equation.

Using point (0, -5):

[tex]\implies a(0-2)^2-3=-5[/tex]

[tex]\implies a(-2)^2-3=-5[/tex]

[tex]\implies 4a-3=-5[/tex]

[tex]\implies 4a=-2[/tex]

[tex]\implies a=-\dfrac{1}{2}[/tex]

Therefore, the equation of the parabola in vertex form is:

[tex]\implies y=-\dfrac{1}{2}(x-2)^2-3[/tex]

#1

Equation

As there is no y inetercept present and the function is same as general quadratic equation y=x^2 just change in coordinates a=1

Final equation

#2

y=a(x-2)²-3

Use (4,-5)

Equation

Answer:

61 Degree Angle

Step-by-step explanation:

Supplementary angles are two angles that add up to 180 degrees. So in this case, 119 + 61 = 180.

[tex]\Large\textsc{answer :}[/tex]

x≤-7

[tex]\Large\textsc{calculations :}[/tex]

First , use the distributive property :

3(x-4)≥5x+2

3x-12≥5x+2

Subtract 5x on both sides :

3x-5x-12≥2

Now , add 12 on both sides :

3x-5x≥2+12

3x-5x≥14

Subtract the x's :

-2x≥14

Divide by -2 on both sides and watch what happens :

x≤-7 (notice that the inequality sign changed from "greater than or equal to" to "less than or equal to")

If we divide both sides of an inequality by a negative number , we change the inequality sign .

[tex]\footnotesize\textit{hope helpful~}[/tex]

Step-by-step explanation:

\Given :

x^{3} +x^{2} -20x

Solution:

x^{3} +x^{2} -20x

taking x common from the given polynomial

⇒x(x^{2} +x-20)=0

⇒x(x(x+5)-4(x+5))=0

⇒x(x+5)(x-4)=0

⇒ x=0 , x+5=0 , x-4=0

⇒x = 0 , x = -5 , x = 4

Answer:

0, x = 4, and x = -3.

Step-by-step explanation:

he zeros of the polynomial function f(x) = x3 − x2 − 12x are x = 0, x = 4, and x = -3. To find these, we can factor the polynomial and set each factor equal to zero. Since x = 0 is already given as a zero, we can factor out x from the polynomial to get f(x) = x(x^2 - x - 12) = x(x - 4)(x + 3) = 0. Thus, the other zeros are x = 4 and x = -3.